Have you ever had to quit doing something for health reasons??

(Have you ever tried quiting something for health reasons?) - is this better?

When I was in "the" university, I used to drink with my friends.

(this is okay, but it could be "together with" and you could emphasize what drink like "drink alcohol together with my friends")

I think it was very fun, so I drank a couple of a week.

(Using "I think it was", is okay, like "I think it was fun". Instead of "very fun" you could use "enjoyable", or "very enjoyable" or just "fun". Just be careful using adjectives. "So I drank a couple "in a week" ) 

However pimples came out on my face. I went to see a doctor.

("Came out" is good but I think "appeared" is more suitable? But if I were the one whose writing this sentence, " However, pimples started to appear on my face and I went to the doctor", just go direct with the sentence so omit "see".)

Doctor said you don't have to drink or eat oily food. And also have to sleep enough. So I stopped drinking to treat my pimple.

("The Doctor said..." always check your articles like "a, an, the". So let me rephrase , "The Doctor said, " You should stop drinking or eating oily food" and I also need to have an enough/good sleep." or "and he also said I should have an enough sleep". So I stopped drinking to treat my pimple.)

After I quit drink, I felt much better

(After I quitted drinking, it felt much better.) In here "it" instead of "I" maybe because it may refer to the idea of "quitted drinking". But nonetheless, It's okay. We can rephrase it to "I feel much better after I quit drinking."

So yeah, overall. It was good just beware of the articles "A, An, The" and your verb tenses and the use of proper words in a sentence more of adjectives. English is my 2nd language, I can't say that I'm an expert nor really good in this. I just corrected words and phrases that I think for me don't go well or sounded right.

Annyeong ^^